MMP.13:2 - Problem

The distribution of the observed records does not itself choose an estimator, an uncertainty statement or a prior. Those additions can produce different useful conclusions from the same data.

The inferential target may also differ from the fitted parameters. A nonlinear function of parameter estimates can give a different answer from averaging that function over a posterior. Shared uncertainty can remain after many repeated readings. A narrow interval for an expected response can coexist with a wide distribution for the next response.

The problem is to construct the inference needed by the receiving use while preserving its sampling, conditioning and approximation assumptions. Changing one of those assumptions must change the relevant calculation, rather than only the qualification attached to an unchanged number.